# Hw3sp00 - COT3100 Spring 2000 S Lang Assignment#3(40 pts Assigned Due 3/8 in class or on 3/9 or 3/10 during your lab class First we define some

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COT3100, Spring 2000 Assigned: 2/28/2000 S. Lang Assignment #3 (40 pts.) Due: 3/8 in class or on 3/9 or 3/10 during your lab class First, we define some terms and notations. Definition. Consider a binary relation R A × B . The inverse of R , denoted R –1 , is a binary relation B × A such that R –1 = {( b , a ) | ( a , b ) R }, that is, R –1 contains pairs of elements which have the reverse order as they are in relation R . (The text calls R –1 the converse of R , denoted R c .) Definition. Let R A × A denote a binary relation. The following relations defined over A are called closures : (a) The reflexive closure of R is r ( R ) = R {( a , a ) | a A }. (b) The symmetric closure of R is s ( R ) = R R –1 . (c) The transitive closure of R is t ( R ) = R R 2 R 3 ... , where R 2 = R R , R 3 = R 2 R , etc., where denotes relation composition. Thus, ( a , b ) t ( R ) ( a , b ) R n , for some n 1 there exist a 1

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Hw3sp00 - COT3100 Spring 2000 S Lang Assignment#3(40 pts Assigned Due 3/8 in class or on 3/9 or 3/10 during your lab class First we define some

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